Given the values of ΔH°_rxn, ΔS°_rxn, and T, determine ΔS_univ and predict whether or not each reaction is spontaneous. (Assume that all reactants and products are in their standard states.) a. ΔH°_rxn = +115 kJ; ΔS°_rxn = -263 J/K; T = 298 K

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1. The first step is to convert the enthalpy change (ΔH°_rxn) from kJ to J, because the entropy change (ΔS°_rxn) is given in J/K. To do this, multiply the given ΔH°_rxn by 1000. So, ΔH°_rxn = +115 kJ * 1000 = +115000 J.

2. Next, calculate the change in entropy of the system (ΔS_sys) using the formula ΔS_sys = ΔH°_rxn/T. Substitute the values of ΔH°_rxn and T into the formula to get the value of ΔS_sys.

3. The change in entropy of the universe (ΔS_univ) is given by the formula ΔS_univ = ΔS_sys + ΔS°_rxn. Substitute the values of ΔS_sys and ΔS°_rxn into the formula to get the value of ΔS_univ.

4. If ΔS_univ is greater than zero, the reaction is spontaneous. If ΔS_univ is less than zero, the reaction is non-spontaneous. If ΔS_univ equals zero, the reaction is at equilibrium.

5. Use the value of ΔS_univ obtained in step 3 to determine whether the reaction is spontaneous or not.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Gibbs Free Energy

Gibbs Free Energy (G) is a thermodynamic potential that helps predict the spontaneity of a reaction at constant temperature and pressure. It is calculated using the equation ΔG = ΔH - TΔS, where ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy. A negative ΔG indicates a spontaneous reaction, while a positive ΔG suggests non-spontaneity.

Entropy (ΔS)

Entropy (ΔS) is a measure of the disorder or randomness in a system. In the context of a chemical reaction, it quantifies the change in disorder between reactants and products. A positive ΔS indicates an increase in disorder, which generally favors spontaneity, while a negative ΔS suggests a decrease in disorder, which can hinder spontaneity.

Enthalpy (ΔH)

Enthalpy (ΔH) is a measure of the total heat content of a system and reflects the energy required to break and form bonds during a chemical reaction. A positive ΔH indicates that the reaction is endothermic, absorbing heat from the surroundings, while a negative ΔH indicates an exothermic reaction, releasing heat. The sign and magnitude of ΔH influence the overall spontaneity of the reaction when combined with entropy changes.